Question 437577
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Flying against a headwind, a plane covers 900 miles in 2 hours. 
The return trip with a tailwind only takes an hour and a half. 
Find the speed of the wind, and the speed of the plane within the air ma
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        The solution by @mananth has too much excessive calculations,

        which means that his computer code, which produces his text and calculations,

        is badly organized and creates  anti-pedagigic narrative.

        As a result,  the solution by @mananth scares readers and is a bad way to teach.


        Below is my solution,  which is a standard treatment of the problem without making unnecessary calculations.



<pre>
Let u be the speed of the plane at no wind;
    v be the speed of the wind.


The groundspeed flying against the wind is 900/2 = 450 mph.

The groundspeed flying with the wind is 900/1.5 = 600 mph.


The equations are

    u + v = 600    (1)   for flying with the wind

    u - v = 450    (2)   for flying against the wind


Adding equations (1) and (2), you get

    2u = 1050  --->  u = 1050/2 = 525 miles per hour.


Subtracting eq(2) from eq(1), you get

    2v = 150  --->  v = 150/2 = 75.


<U>ANSWER</U>.  The speed of the plane at no wind is 525 mph.  The rate of the wind is 75 mph.
</pre>

Solved by the most straightforward way, &nbsp;without making unnecessary calculations.